attitude accuracy study for the earth observing system (eos) am-1 spacecraft

7/29/2019 Attitude Accuracy Study for the Earth Observing System (EOS) AM-1 Spacecraft

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Attitude Accuracy Study for the Earth Observing System(EOS) AM-1 Spacecraft*JamesD. Lesikar11

COMPUTER SCIENCESCORPORATIONLanham-Seabrook, Maryland, USA 20706Joseph C GarrickNATIONAL, AERONAUTICS ANDSPACE ADMINISTRATIONGODDARD SPACE FLIGHT CENTERGreenbelt, Maryland, USA 20771

ABSTRACTEarth Observing System (EOS) spacecraft will makemeasurements of the earth's clouds, oceans,atmosphere, land and radiation balance. These EOSspacecraft are part of the National Aeronautics andSpace Administration (NASA) Mission to Planet Earth,and consists of several series of satellites, with eachseries specializing in a particular class of observations.This paper focuses on the EOS AM-1 spacecraft, whichis the first of three satellites constituting the EOS AMseries (morning equatorial crossing) and the initialspacecraft of the EOS program. EOS AM-1 has astringent onboard attitude knowledge requirement, of36/41/44 arc seconds (30) in yaw/roll/pitch,respectively.During normal mission operations, attitude isdetermined onboard using an extended Kalmansequential filter via measurements from two charge-coupled device (CCD) star trackers, one Fine SunSensor, and an Inertial Rate Unit. The AttitudeDetermination Error Analysis System (ADEAS) wasused to model the spacecraft and mission profile, and ina worst-case scenario with only one star tracker inoperation, the attitude uncertainty was 9.7/11.5/12.2arc seconds (30) in yaw/roll/pitch. The quoted resultassumed the spacecraft w as in nominal attitude, usingonly the 1-rotation per orbit (rpo) motion of thespacecraf&about the pitch axis for calibration of thegyro biases. Deviations from the nominal attitudewould show greater attitude uncertainties, unless

calibration maneuvers which roll and/or yaw thespacecraft have been performed; this permitscomputation of the gyro misalignments, and theattitude knowledge requirement would remain satisfied.

INTRODUCTIONPurpose and M ethodologyAttitude error analysisstudies are needed to determinewhether the EOS-AM1 satellite can meet its attitudeaccuracy requirements using its onboard computer andsensor complement.The present study determines:1. The accuracy to which attitude sensor and gyro

calibrations can be performed.2. The expected attitude determination error for

various sensor combinations.The Attitude Determination Error Analysis System(ADEAS) is an analysis software tool that provides ageneral-purpose linear error analysis capability forvarious spacecraft attitude geometries, sensorcomplements, and determination processes. Anappropriate NAMELIST setup permits ADEAS tomodel the salient features of the EOS AM-1 spacecraftand mission profile.

Thiswork was supportedby the National Aeronautics and Space Administration (NASA)/Goddard Space FlightCenter (GSFC), Greenbelt, Maryland, under Contract NAS 5-3 500.

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BackgroundEOS-AM1 is the first of three satellites constitutingtheEOS-AM (morning equatorial crossing) series insupportof NASA's "Mission to PlanetEarth"and is theinitialspacecraftof the EOS program.EOS-AM1 will be launched from the Western TestRange, Vandenberg Air Force Base, California, withthe General Dynamics Atlas IIAS launch vehicle inJune 1998. EOS-AM1 has a planned mission Metimeof 5 years.The initial parking orbit has an altitude of 525 by 705km with an inclination of 98.2 deg. After a series oforbit-raising maneuvers, the mission orbit will bedescribedas follows:- Sun-synchronous polar- Inclination= 98.2 deg-- 705 km altitude, circular-

10:30 a.m. f 15 min descending node, local meansolartim!Groundtrack repeats in 233 orbitdl6 days, wthf20km cross-track error at node crossings

Spacecraft Attitude Control SystemThe EOS-AM1 spacecraft is being manufactured byLockheed-Martin, Valley Forge, Pennsylvania. Thespacecraft will have the following complement ofattitudesensor and actuator hardware:- CCD star tracker (CCDST) (2)- Earth scanner assembly @SA) (2)- Fine sun sensor(FSS) 1)- Three axis magnetometer(TAM)(2)- CoarseSun sensor CSS) (9pairs)- Inertial rate unit0 6 axes)- Reactionwheels(4)- Magnetic torquer rods 3)Immediately afw launch, the onboard computer, v iathe attitude thrusters, uses ESA data to roll and pitchthe spacecraft to acquire the Earth and to orient thespacecrafbody 2 xis to nadir-pointing, then performsorbital gymompassing to align the body X axisroughly parallel to the velocity vector. When in normalmission mode, attitude is determined via sequentialfilterusing the wo CCDSTs (theFSS can substitute forone CCDST if one ails) and the IRU and is controlledby the reactionwheels.

The onboard computer uses an extended Kalmansequential filter to determine attitude during normalmission mode operations. The statevector is composedofan attitude quaternion and the IRU ate biases. Starobservationsare taken from alternate star trackers, anda particular star is used as a valid observation only if(1) it is in the onboard star catalog, and (2) it is visiblein tw o consecutive observationsby the same star tracker(16.384 sec later). The attitude propagation cycle timeis 0.512 sec, based on using filtered gyro rates (themeasured gyro data are available every 0.128 sec).Attitude RequirementsThe spacecraft attitude is described by a 3-1-2 (yaw-roll-pitch) Euler rotation sequence, which relates thebody coordinate system (BCS) to the orbital coordinatesystem (OCS). The spacecraft null attitude has the BCScoincide with the OCS. The OCS is a rotatingcoordinate system. The OCS coordinate axes originatein the spacecraft's center of mass. The +Z axis pointsto the geocenter, the +Y axis points to the negativeorbit normal, and the +X axis completes theorthogonal triad. The null attitude, in which the threeEuler angles are zero, has the OCS and BCS coincide.Null attitude is the desired attitude during normalmission mode.The attitude knowledge requirements (the accuracy ofthe attitude determination) during normal missionmode are specified to be:---

41 arc seconds in roll (30)36 arc sec in yaw (30)44 arcsec n pitch (30)

Sources of Attitude ErrorWhen EOS-AM1 is in normal mission mode, thefollowing quantities influence the sequential filterattitude error:0 IRU (a.k.a. gyros)- Rate bias errors (deglsec)- Scale factor errors (dimensionless)- Alignment errors (deg)- Gyronoisesuchas

a) Inverse gyro bias noise time(l/=)b) Attitude error vector noise(deg/sec'/2)

c) Gyro bias noise (deglsec?)

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* CCDSTs- Alignment errors (deg)- Measurement noise (deg)- Field of view errors

* FSS- Alignment errors (deg)- Measurement noise (deg)- Field of view errors

Kalman filter tuning parameters. Same units as:-- Gyro bias noise (de g /~ ec~~ )Attitude error vector noise (deg/~ec '~ )

THEADEAS MODELWhat AI)EAS Can DoADEAS is capable of modeling, on option, either thebatch weighted least-squares filter or the sequentialfilter with Kalman gain. The latter mode is chosen forthe analyses presented here. The various gyro noiseparameters, CCDST and FSS measurement noises, andKalman filter tuning parameters are user-input and areheld constant for each run of ADEAS. The attitudedetermination uncertainty is always solved for; aninitial (a priori) attitude uncertainty is specified at thebeginning of the run and is usually chosen to be largeto permit the filter to properly converge by avoidingnumerical instabilities.

The IRU rate bias, scale factor and alignment errors,CCDST alignment and field-of-view (FOV) errors, andFSS alignment and FOV errors, can either be held atconstant value (i.e., not solved for) or solved for, givena set of a priori starting values. Quantities referred toas "consider" parameters are held at constant value; theterm "pefiect" is sometimes used in this paper to denotea consider parameter with a value of zero (no error).Conversely, 'Solve-fory'parametersevolve with time (asmore measurements are made) and use the a priorivalues as initialestimates fortheparameters.This report is primarily concerned with evaluating theinfluence of IRU biases and scale factors and IRU,CCDST and FSS misalignments on the attitudeuncertainty. The CCDST and FSS FOV errors are"perf&%" (FOV errors are errors resulting fromcomponent alignments within the sensor, opticaldistortions,and manufkturingaberrations.)

Orbit Model UsedFor purposes of internal propagation, the model orbithas the following Keplerian orbital elements, whichsatisti, a 10:30 a.m. mean local time descending node(Reference 1):

Epoch 980630.040000Semimajoraxis 7083.14km

0.0001ccentricityInclination 98.2 degRight ascension

255 356degArgument of perigee 90.0 degMean anomaly 270.0 deg

of ascending node

All orbit perhubative forces that can be modeled byADEAS are enabled. These forces include the Earthoblateness J2 effect, solar and lunar point massperturbations, and atmospheric drag with a spacecraftballistic coefficient of 2.2.Star Catalog UsedA prototype spectral response curve (color index) forthe Ball CT-601 solid state star tracker was obtainedfrom the Submillimeter Wave Astronomy Satellite(SWAS) project. This curve is necessary to convert starcatalog visual (V)magnitudes into instrumental (I)magnitudes.The prototype SWAS pectral response curve isV- Iswm = 0.0043S3-0.0015S2+ 0.0214s - 0.1733where S s the spectral index. For the Sun, a spectralclass G2 star, S s equal to 4.2.The source catalog for creating the prototype EOS runcatalog is the SKYMAP Master Catalog version 3.7, asequential file that contains approximately 248,000stars. The SKYMAP library routine CAT then uses theprototype SWAS spectral response curve to convert V-magnitudes into I-magnitudes. It then assembles anEOS specific ntermediate run catalog in a direct-accessformat containing stars brighter than I-magnitude 9.Intermediate catalogs are created taking into accow3tthe following criteria for each star:-- Excludes stars with V-magnitude uncertainties

Limited to I magnitudes ranging from 2 to 6greater than0.1

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Excludes variable stars with %magnitudeamplitudes greater than0.1Excludes multiple star systems with the twobrightest components having V-magnitudeWerences less than5.0Excludes stars with proper motions greater than0.7 arc sec per yearExcludes stars with position uncertainties greaterthan3.0 arc secUses near neighbor checks such that no s t a r iswithin 0.25 degree and iswithin 3 I-magnitudes ofthe candidate star

Position Accuracy30,w.r.t.mountingMagnitudeAccuracy3aNoise EquivalentAngle (NEA)

The final sequential catalog contains 2197 stars in anASCII-readable format. Another catalog was thenproduced in direct-access MMS star record format byusing the SKYMAP Library routine CAT with theASCII catalog as input. This direct access catalog is theNe that is actually used by ADEAS for EOS-AM1attitude error analysis studies. Further details on thecreation of this catalog, and its comparison to the EOSstar catalog created in 1990by General Electric, can befound in Reference 2.

Magnitude Magnitude+2.0 to +4.0 to+4.0 +5.710arc sec 16arc sec

0.25 0.5

3.0 arc sec 5.0 arc sec

Alignment AnglesReference3 is the primary source of sensor parameterspresented here. Reference 4 only slightly modifies theFSS performance requirements into a form that isidentical to those for the Upper Atmosphere ResearchSatelliteWARS) (Reference 5).AlI sensor boresights point in the +Z direction for eachrespective sensor coordinate system. Euler rotations inthe 3-1-3 sequence transform from the BCS coordinatesinto each sensor coordinate system. Table 1 shows therotation angles and Table 2 shows boresight unitvectors expressed in BCS coordinates.

Table 1. Sensor Euler Rotation AnglesSensor 2nd 3rdRotation Rotation

Charge-Coupled Device Sta r Trac kersThe two Ball CT-601 CCDSTs are mountedsymmetrically about the BCS Y-2 plane, such that astar that appears'in the FOV of CCDSTl will, in thenormal mode of the attitude control system, appear inthe FOV of CCDST2 after about one-third of an orbit.Each of the CCDSTs has an 8-deg by 8deg FOV, issensitive to stars with I-magnitudes from +2.0 to +5.7,and can track five stars simultaneously. The majorconstraint to tracking to specification for theseCCDSTs is that all stars within a 0.25 deg radius of acatalog star need to be at least 3 magnitudes dimmer.The CCDSTs are unreliable for the Sun within 45 degof the CCDST boresight, or for the Moon within 17 degof the boresight.Current understanding of the CCDST has it raster scanfrom "top" to %ottom" until the first five guide starsare encountered. This approach differs from the twoADEAS CCD options: (1) choosing the five brightests t a r s in the FOV and (2) performing a spiral scan aboutthe boresight until five s t a r s are encountered. Since 4-pi steradiansequals 41252.9 deg., the sky is covered by645 CCD FOVs, for an average of 3.4 stars if theprototype EOS catalog with 2197 stars is used; so onaverage the chosen ADEAS option is unimportant, andoption 1 is used arbitrarily. Table 3 has the requiredCCDST performance.

Table 2. Sensor Boresight Vectors (BCS)Here it is assumed that the position accuracy and NEAare on a per a x i s basis. The star catalog positionuncertainty (Reference 6, per axis, 3 0 ) is taken to be 3arc sec.One ADEAS input is the standard deviation ofmeasurement noise, which is computed for dim andbright stars, depending on whether a star is less thanor

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greater thanI-magnitude 4 n brightness. The standarddeviation of measurement noise is calculated by takingthe star tracker position accuracy, noise equivalentangle, and star catalog position accuracy in quadrature.Standard deviation of measurement noise(bright stars, 30)= [lo2+ (3 x 3)2 + 32]1" = 13.78arc s 8 ~=6.683 radStandard deviation of measurement noise(dim stars, 30)= [162+ (3 x 5)2 + 32]'" = 22.14arc sec

= 1.073x 10"' radThe 30 lignment uncertainty, per axis, is 0.05deg.R ne Sun SensorThe Adcole FSS (Model 42050 sensor and Model42070 electronics) is composed of two orthogonallymounted single-axis Sun sensors. Each single-axis Sunsensor consists of two reticles: a fine reticle and acoarse reticle. The coarse reticle pattern is gray-codedand encodes the coarse angle over the entire FOV. Thefine reticle patterns and the resultant photocell currentsare used to generate fine-angle data. The overall FOVis 64 deg square. The output resolution is 14 arc secper least significant bit. The overall accuracy for a 32-deg half-cone is 60 arc sec, and the accuracy betweenthe half-cone of 32 deg and the FOV of 332 deg is 120arc sec.As the above description also applies to the UARS FSS,we may extract the standard deviation of measurementnoise from Reference 5,which gives the value 75 arcsec or 0.02083 deg for 3 0 uncertainty. The 3 0alignment uncertainty, per axis, is0.05 deg.Inertial Rate UnitThe Kearfott IRU is composed of three independentchannels, each channel having one two-axis gyro andassociated electronics. Under command, the IRU issensitivetoeither of two rate ranges:- Low Rate: fo.11 deglsec maximum rate, with a

scale factor of 0.05arc sec/pulse for incrementaloutputHigh Rate: 32.0 deglsec maximum rate, with ascale factor of 0.8 arc sec/pulse for incrementaloutput

-

The analog rate output range isf2.0 eglsec.ADEAS does not model low or high IRU rates, or theanalog output, since ADEAS uses engineeringunitsinternally, rather than counts or pulses.The following30 ncertainties are allocated per axis:- Noise (white) O.OOO1 deglsecIn- Noise (drift) 0.00138

= 6.3889~o-' degl sec3I2- Alignment 0.1deg- Bias 2.0deglhr

= 5.5555 x deglsecFrom Reference 5, the 30 uncertainty in the standarddeviation of the scale factor, per axis, is 1.4 x lo5( U A R S value). The inverse gyro bias noise timeconstant is assumed to be 0.0, an appropriate value forwhite noise.Kalman Filter ParametersThe Kalman filter parameters were chosen to have thesame values as the attitude error vector noise (whitenoise) and gyro bias noise (drift noise) tabulated for theIRU above. No attempt was made in this analysis totune these parameters for optimum convergence.

ESTIMATED SENSOR UNCERTAINTIESMethodologyNumerous runs of duration 6000 sec (slightly longerthan one orbital period) were performed, with CCDSTand FSS sensor data simulated at 10-sec intervals.Various combinations of solve-for and consider sensorparameters were used, with a priori and consider valuestaken from the prelaunch errors of Table 4 below.CCDSTl was assumed to be "perfect" and wastherefore the reference coordinate system for thecalibrations. The initial attitude uncertainty was set to999.0deg to ensure that the starting attitude knowledgewas unknown.Throughout this section and the next, two systems ofunits are used, the ADEAS inputdoutputs (in degreesand degrees per second) and units more suitable forinterpretation and comparison wth missionrequirements (arc seconds and arc seconds per hour).

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Table 4. Prelaunch Uncertainties ( 3 0 )I Sensor I Quanti I Value I Equivalent I Maneuver# Time tand into runDescription (sec)Maneuver 1 0

I I I ValueInertial I Rate Biases I 5.555E-4 I 7200Roll Rollrate(deg) (deglsec)0.0 0.0eferenceUnit

(IRU)

deg/sec arcseclhr

Scale Factor 1.4E-5 n/a (35 eg roll) 1800 0.0 8.33E-32400 5.0 -8.33E-33600 -5.0 8.33E-34200 0.0 0.0

Calibration results for CCDST2 and the FSS did notimprove (results were much larger than the prelaunchvalues, by up to a factor of 3), and the attitudeuncertainties would not shrink below about 0.3 de&unless IRU rate biases were solved-for simultaneously.This empirical observation makes sense. Duringperiods when no sensor data are available, the attitudeis propagated using the IRU bias, the fixed biasuncertainty, and noise. When the CCDST2 andFSS dohave data, their observation vectors confiict with thatexpected from the dynamically modeled attitude, andthe CCDST2RSS alignment errors grow tocompensate. The necessity to continually solve for IRUbiases was independent of the size of the biasuncertainties when specified as consider parameters, asthe computed CCDST2RSS alignment errors remainedlarge, as did the attitude uncertainties.

MisalignmentCC D Star

Attempting to solve for all parameters at once took aninordinate amount of time, and the IRU scale factoruncertainties did not change at all. Thus, calibrationruns solved for IRU rate bias errors and IRU, CCDST2,andFSS alignment errors.

0.1 deg 360arcsec

Calibration runs were performed for 14 differentattitude maneuver scenarios. Table 5 below lists thedetails of three schemes. Maneuver 1 is the nadir-pointing 1 rpo case, which is the nominal attitudeprofile. Maneuver 2 is a 35 deg roll offset fromnominal, not unlike what UARS used for its on-orbitcalibratioa Maneuver 3 is a 320 deg roll offset versionof Maneuver 2. The table indicates the attitude anglesand rates at the beginning and end of the run, alongwith times at which new attitude rates are commandedandtheattitudeoffsetsat those times.

Trackers(CCOST)Fine Sun

Table 5. Attitude Maneuver Profiles

Misalignment 0.05 deg 180 arc sec

Sensor(FSS)

_ -(I rpo) I 6000 I 0.0 I 0.0Maneuver2 I 0 I 0.0 1 0.0

Misalignment 0.05 deg 180 arc sec1 6000 I 0.0 I 0.0Maneuver3 I 0 I 0.0 I 0.0

roll) -3.33E-24200

0.0

CCDST nd FSSAlignment UncertaintiesThe computed results for CCDST2 uncertainties wereindependent of the maneuver scheme used, as onewould expect. FSS uncertainties did vary betweenmaneuver schemes, but this variation can be attributedto differing periods of Sun visibility (23 minutes forManeuvers 1and 2 and 20 minutes for Maneuver 3), sodiffering amounts of datawere available for calibration.For example, the FSS uncertainties from Maneuver 3were 20 percent larger thanfor Case 1of Table 6.The results presented in Table 6 were all derived fiomManeuver 1, a nominal pointing scenario. Case 2 isidentical to Case 1, except that it is a 12,000-sec run.Case 3 used the results of Case 1 as a prioriuncertainties, which illustrates that repeated sensoralignment calibrations will result in smaller alignmentuncertainties. Thus, longer spans of data,and accurateestimates of alignments after a calibration run, willresult in subsequent calibration runs having smalleruncertainties. In principle, with sufficiently long runs,these misalignment errors can be made arbitrarilysmall. However, the overall sensor uncertainty will notnecessarily behave similarly, since the sensormeasuTement noises become the dominant effect. Theprelaunch alignment uncertainties are shown in Table 6for comparison.The X, Y, and 2 components of CCDST2 and FSSalignment uncertainties need to be interpreted carefully,as they represent uncertainties in rotation angles aboutthe nominally aligned sensor coordinate system foreach sensor, with 2 eing the boresight vector.

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Table 6. Alignment Uncertainties (arc sec, 30)

PrelaunchConsider

IRU Alignment and Rate Bias Uncertainties

"Perfect" Attitude(Consider=O) Uncertainty

Table 7 s a comparison of the prelaunch IRU rate biasuncertainties and the IRU misalignment uncertaintieswith the uncertainties computed for the three attitudemaneuver calibration schemes of Table 5.

ManeuverSchemeandIRU Rate Bias IRU AlignmentUncertainty Uncehinty(arc sec/hr. 3a) (arc sec.3dDescription

Prelaunch

From Table 7we can draw the following conclusions:

. . . -X I Y I z X l Y l Z

7200 I 7200 I 7200 360 I 360 I 360

1.The IRUmisalignment errors cannot be improvedunless maneuvers that deviate from nominal attitude(schemeNo. 1)are performed.

CCD2 MlAsFSS M/AsIRU RBs

2. Larger calibration maneuvers result in smallerIRUalignment uncertainties.

IRU SFsIRU M/AsIRU MlAs 601

3. Larger calibration maneuvers result in smallerIRUX- andZ-axisate bias uncertainties..TheIRUY-axisate bias uncertainty is unaffectedbv the mamitudeof the calibration maneuver.

The latter conclusion is explained by maneuversdecreasing the magnitude of the Y-axis ngular rate,whereas an increase in the rate would be required toreducethe rate bias uncertainty.

ESTIMATED ATTITUDE UNCERTAINTIESResults Using Prelaunch Alignment UncertaintiesAttitude was solved-for using various combinations ofprelaunch consider values and "perfect" values for theattitude sensors and IRU parameters. This was done togain some appreciation of which consider parametershad the most impact upon the computed attitudeuncertainty. Table 8 indicates that prelaunch considervalues for the IRU biases are the greatest singlecontributor, followedby the CCDSTs and FSS, the IRUmisalignments, and, finally, the IRU scale factors,which had an 8 arc sec level of uncertainty.

Table 8. Attitude Errors With PrelaunchUncertainties (IRU Bias not Solved For)Solve-for'arameters

Attitudeonly

LEGEND:

values I . I (arcsec,%)IRURBs I 673IRU SFsIRU M/ASCCDl WASCCD2 WASFSS MIAsIRUSFsIRU MlAsCCD2 MIAsFSSMlAs I IIRURBs I CCDl MIAs I 605IRUSFs I CCD2M/As IIRUMlAs I FSSMlAs ICCDl MIAs I IRU RBs I 292

IRUM/As 1 IRURBs I 88

I FSSMlAs IIRU SFs I IRURBs I 8I 1CCDPWASI FSSM~AS- IRBs: Rate Biases SFs: Scale FactorsM/As: Misalignments CCD: CCDST

Y

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Attitude and IRU biases were also solved-for,mimicking the onboard computer and its sequentialfilter and using prelaunch consider values for all othersensors, with differing combinations of the CCDSTsand FSS functioning. These combinations are shownin Table 9. The first case is for all three sensors "on"as a baseline, even though this is not a flight mode.The other three combinations shown are flight modes,namely CCDSTl and 2, CCDSTl and FSS, andCCDSTl by itself. As one would expect, the last caseshows the largest uncertainty.

Table 9. Attitude Errors With PrelaunchUncertainties (IRU Bias Solved For)Solve-forParameters

AttitudeandIRU RBs

I LEGEND:

PrelaunchConsider ValuesusedIRU SFsIRU WASCCDl MIAsCCD2 M/AsFSSWASIRUSFsIRU M/AsCCDl MIAsCCD2 MIAsIRU SFsIRU M/AsCCDl MIAsFSS M/AsIRUSFsIRUMIAs I I I

SensorCombinationUsedCCDlCCD2FSS

CCDlCCD2

CCDlFSS

CCDl

AttitudeUncertainty(arc sec, a)292

292

288

317CCDl MIAs I IRBs: Rate Biases SFs: Scale Factors I

I WAS: Misalignments CCD: CCDST IThe root sum square ( R S S ) uncertainties shown inTables 8 and 9 were for the attitude uncertainties at theend of each respective ADEAS run.Results Using Solved-For Alignment UncertaintiesAll of the results in this section were based on asequential filter, solving for the attitude and IRU ratebias uncertainties, as does the actual EOS-AM1onboard computer. The computed attitudeuncertainties are with respect to the BCS. The attitudeuncertainties based on the prelaunch uncertaintiesutilize the uncertainties for all sensors (CCDSTl,CCDST2, FSS, nd IRU misalignment errors), whereasthe attitude uncertainties computed using thecalibration profile based on Maneuver 1, also known as"on-orbit" nominal, assume that the CCDSTlalignment is perfectly known. The prelaunch considervalues for the IRU scale factor errors were used in allcases.

The calibration profiles based on Maneuvers 2 and 3were also applied against Maneuver 1, with no changein results, and are therefore not shown in Tables 10through 12.Use is also made of ADEAS' capability to display theerror budget for each computed uncertainty. Thisshows the contribution of each consider parameter,measurement noise, and dynamic noise to the overallerror.Two CCDSTs and One FSSThis s not a flight mode for the onboard computer, butthese solutions are provided as a baseline . The attitudeuncertainties based on the prelaunch sensor alignmentuncertainties are dominated by the CCDSTl andCCDST2 uncertainties (large), whereas the attitudeuncertainties based on the 1-rpo calibration aredominated by CCDSTZ misalignment uncertainties(small), closely followed by measurement noise. Use ofthe 1-rpo calibration profile easily satisfies missionrequirements forEOS-AM1 n the nominal attitude.Table 10. Attitude Error for CCDSTl & 2, FSS

T ~ QCDSTsThe nominal sensor complement for onboard attitudedetermination is two CCDSTs. These numbers do notdiffer at all from those of Table 10, and the errorbudgets are identical. Thus the conclusions for twoCCDSTs are identical to those presented for twoCCDSTs and the FSS,except that the FSS would notimprove the attitude solution. This is as one wouldexpect intuitively.One CCDST and One FSSThis is the first contingency mode for the onboardcomputer, in case one CCDST fails. The attitudeuncertainties based on the prelaunch sensor alignmentuncertainties are dominated by the CCDSTl

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uncertainties (large), closely followed by the FSSuncertainties. The attitude uncertainties based on the1-rpo calibration are dominated by measurement noise.Use of the 1-rpo calibration profile easily satisfiesmission requirements for EOS-AM1 in the nominalattitude, and the error is only slightly worse than thecaseswith two CCDSTs.

CalibrationProfileMission

Table f 4 . Attitude Error for CCDSTl & FSSManeuver Attitude UncertaintyProfile (arc sec, 3a)X I V I ZI I

On-Orbit(1-RPO)

1 Requirement I N/A 1 41.0 I 44.0 ~ 36.0 1Prelaunch Maneuver 1Values ( I -RPO) 176.0 155.0 166.0

IManeuver 1(1-RPO) 11.5 12.2 9.7

PrelaunchValues

OneCCDST

Maneuver I(1 -RPO) 180.0 180.0 180.0

This is the second and last contingency mode for theonboard computer, in case one CCDST and the FSSboth fail. The error budgets for the various casesparallel those listed in the previous section, ignoring allreferences to the FSS. Again, use of the 1-rpocalibration profile easily satisfies mission requirementsforEOS AM-1 in the nominal attitude. Notice that thelack of FSSmeasurements did not change the level ofuncertainty from the CCDST/FSS scenario.

On-Orbit(1-RPO)

Table 12. Attitude Enor for CCDSTl Only

Profile ProfileMissionRequirement NIA

Maneuver1(1-RPO) 11.5 12.2 9.7

CONCLUSIONSRelative to one star tracker, the alignment uncertaintiesof the other star tracker and the fine Sun sensorbecomesmaller asymptotically with the use of longer spans ofsensor data. These results are independent of the

attitude maneuver scenario, except for the maneuver'sinfluence upon the length of time that the Sun is visibleto the FSS.Attitude maneuvers that deviate from nominal pointingare necessary for improving the IRU alignmentuncertainties. The larger the attitude manewers, thesmaller the IRU alignment uncertainties, which in turnreduces the IRU rate bias uncertainties. The smallerthe IRU rate bias uncertainties, the more accurate willbe the propagated attitude solution in the onboardKalman sequential filter during those times whensensor observations are unavailable. The statements ofthis and the preceding paragraph, although derivedfrom the particulars of the EOS-Ah41 mission, are trueindependent of the details of a particular satellite.Since performing a S O deg roll maneuver reduces theIRUalignment uncertainties by a factor of 10 or more,and reduces the IRU rate bias uncertainties by a factorof 50 or more (in both cases relative to the prelaunchuncertainties), it is recommended that attitudecalibration maneuvers have at least a 20 deg excursionfrom the nominal 1-rpo attitude profile and, if possible,that they include both roll and yaw maneuvers.If no calibrations are pedormed, and the EOS-AMIsequential filter is used to solve for the attitude and IRUrate biases, then the RSS absolute attitude uncertaintyis of the order of 300 arc sec, which is far in excess ofthe mission requirements. Therefore, some attempt atcalibration must be made. A calibration profile solelybased upon the nominal 1-rpo motion will SUffiGe forall sensor combinations.As suggested by data presented in this report,calibration maneuvers should have a minimum of 20deg in roll and yaw, which would provide robustness tothe accuracy of attitude solutions for large deviationsfrom nominal 1-rpo pointing. Previous analyses forother missions have indicated that 30-deg maneuversabout each axis are needed to achieve the best results.As the EOS ohitswill have plenty of star observationsfor attitude determination, the choice of one CCDST asbackup to the two-CCDST configuration is adequate.TheFSSwould not improve the attitude solution unlessstar observations were unavailable due to S dmooninterference in the CCDST, during times when the Sunisvisible to the FSS.The results of this analysis show that the onboardattitude determination function will be more thanableto meet the uncertainty requirements.

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REFERENCES1. Computer Sciences Corporation, SEAS Quick Note

QN-52473-06, "Propagation of Earth ObservingSystem @OS) Epoch State and Force ModelErrors," A. Schanzle (CSC) and J. Rovnak (CSC),August 7,1992

2. Goddard Space Flight Center, Flight DynamicsDivision 553-FDD-94/003ROUDO, Earthobserving System (EOS) Flight DynamicsAnalysis Task Prototype Star Catalog, J. Lesikar(CSC) and S. Barriga (CSC), prepared byComputer Sciences Corporation, February 1994

3. General Electric Astro-Space Division, EOS-AM 1Spacecraft Guidance, Navigation and ControlSubsystem Preliminary Design Review, September23-24, 1992.

4. Martin-Marietta Astro-Space Division, DR SP-601, "Performance Specification, Guidance,Navigation & Control (GN&C) Subsystem forEOS-AM," July 22, 1993

5. Goddard Space Flight Center, Flight DynamicsDivision, FDD/554-90/057, Upper AtmosphereResearch Satellite (UARS) 1990 Flight DynamicsAnalysis Report 7: UARS Ground DefinitiveAttitude Determination Analysis, J. Golder (CSC)and M. Nicholson (CSC), prepared by ComputerSciences Corporation,January 1991

6. Goddard Space Flight Center, Flight DynamicsDivision, 553-FDD-93/013ROUDO, 1993 StarCatalog Analysis Report 1: SKYMAP MasterCatalog Data Analysis,M. Slater (CSC), A. Miller(CSC), prepared by Computer SciencesCorporation, February 1993

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